Welcome to YT & congrats on the new pup!
Please don't put a collar on a Yorkie- only a harness. They have delicate tracheas and are prone to injury there.
I would be careful with bigger dogs in the home also, they can unintentionally harm them will playing.
That price seems VERY low for a Yorkie! In Missouri I have paid a great deal more mine.
As far as shampooing - I agree with the others that Yorkie Splash and Shine is very good. I do have 2 that have itchies and they only get bathed in the purple no more tears Johnson baby Shampoo (per the Vet) and they do fine.
We need pictures of your sweetie!